How do you use the properties of logarithms to rewrite and simplify the logarithmic expression of #log2 (7^2 * 4^7)#?

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Answer 1 · 2015-07-05T22:36:51

#log_2(7^2·4^7) = 2log_2 7 +14log _2 2#

First Property: #log_b(x y) = log_b x+log_b y#

So

#log_2(7^2·4^7) = log_2(7^2) + log_2(4^7)#

Second Property: #log_bx^r = rlog_b x#

So

#log_2(7^2·4^7) = log_2(7^2) + log_2(4^7) = 2log_2 7 + 7log_2 4#

But #4 = 2^2#, so

#log_2(7^2·4^7) = 2log_2 7 + 7log_2(2^2)#

#log_2(7^2·4^7) = 2log_2 7 + 14log _2 2#